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What is the point-slope equation of a line with slope -3 that contains the point [tex][tex]$(-8,-4)$[/tex][/tex]?

A. [tex][tex]$y-4=-3(x+8)$[/tex][/tex]

B. [tex][tex]$y-4=-3(x-8)$[/tex][/tex]

C. [tex][tex]$y+4=-3(x+8)$[/tex][/tex]

D. [tex][tex]$y+4=-3(x-8)$[/tex][/tex]

Sagot :

GinnyAnswer
Sure! To find the point-slope equation of a line that contains the point [tex]\((-8, -4)\)[/tex] with a slope of [tex]\(-3\)[/tex], we can use the point-slope form of a linear equation. The point-slope form is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope of the line.

Given:
- The point [tex]\((x_1, y_1) = (-8, -4)\)[/tex]
- The slope [tex]\(m = -3\)[/tex]

Let's substitute these values into the point-slope form equation:

[tex]\[ y - (-4) = -3(x - (-8)) \][/tex]

Simplifying the equation:

[tex]\[ y + 4 = -3(x + 8) \][/tex]

Thus, the point-slope form of the line is:

[tex]\[ y + 4 = -3(x + 8) \][/tex]

So, the correct answer is:

C. [tex]\( y + 4 = -3(x + 8) \)[/tex]
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